In this unit we will use a study of the sample proportion to draw conclusions about the population proportion.

.

Sampling Techniques

.

A good sample should be representative of the population.
.

Random Sample

… A randomisation method is used to identify the members to be included in the sample

… Each member of the population has the same probability of being selected for the sample

… A common method is to use a computer/calculator to generate a list of random numbers
… … where each number corresponds to a member of the population.
.

Example 1

A researcher wishes to evaluate how well the local library is catering to the needs of a town’s residents. To do this she hands out a questionnaire to each person entering the library over the course of a week. Will this method result in a random sample of the town? What is a better method?

Solution

The sample would only contain people who use the library so this is not random.

The researcher should select people randomly at different locations around the town

.

Systematic Sample

… This assumes the members of the population are randomised and then placed in some sort of order

… Every k member of the population is chosen for the sample. {where k is some integer|

… Eg every 10th member is selected
.

Example 2

A production line produces chocolate bars. Every 15th chocolate bar is selected and tested to ensure it passes quality control. Will this method result in a random sample? What assumption has been made?

Solution

For most situations, this would produce a random sample.

The assumption is that there is no pattern to the way chocolate bars end up on the production line.

For example, if the chocolate bars came out of a mold with 15 slots, then every 15th bar might have come out of the same slot in the mold.

.

Stratified Sample

… This method is appropriate when there are subgroups within the population

… The subgroups may have a differing likelihood of scoring a success

… A random sample is taken from each subgroup in proportion to the size of that subgroup
.

Example 3

A sample of 10 students is to be selected from a group of 200 students, of whom 113 are in Year 11 and 77 are in Year 12.

How many students should be selected from each Year 11 and Year 12 according to Stratified Sampling.

Solution

The proportion of Year 11s in the population is $\dfrac{123}{200} = 0.615$

.

So the number of Year 11s for the sample is:

$0.615 \times 10 = 6.15$

so 6 Year 11 students

.

So the number of Year 12s for the sample is:

$10 - 6 = 4$

so 4 Year 12 students

.

Self-Selected Sample

… participants volunteer to be in the sample

… samples obtained using this method are almost never representative of the total population

… phone-in polls or online competition voting are examples of this style of sampling

.

Using the Casio Classpad

We can use the Classpad to produce a list of random numbers
This list can then be used to select a random sample from a population

Press KEYBOARD

Tap down arrow on bottom left of keyboard screen

In CATALOG, select RANDLIST(

Type: 10, 1, 30)

Press EXE

RANDLIST(10, 1, 30) will produce a list of 10 random numbers between 1 and 30